| 書目名稱 | The Implicit Function Theorem | | 副標題 | History, Theory, and | | 編輯 | Steven G. Krantz,Harold R. Parks | | 視頻video | http://file.papertrans.cn/912/911842/911842.mp4 | | 圖書封面 |  | | 描述 | The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis.There are many different forms of the implicit function theorem, including (i) the classical formulation for C^k functions, (ii) formulations in other function spaces, (iii) formulations for non- smooth functions, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash--Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume.The history of the implicit function theorem is a lively and complex story, and is intimately bound up with the development of fundamental ideas in analysis and geometry. This entire development, together with mathematical examples and proofs, is recounted for the first time here. It is an exciting tale, and it contin | | 出版日期 | Book 2003 | | 關鍵詞 | Differential Geometry; Partial Differential Equations; Real Analysis; cls; analytic function; differentia | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-0059-8 | | isbn_ebook | 978-1-4612-0059-8 | | copyright | Springer Science+Business Media New York 2003 |
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